1. Field of the Invention
The present invention relates to apparatus and methods to encode information to reduce a probability of errors in a transmission and/or a recording (storage) of the information.
2. Description of the Related Art
In magnetic recording, various sources of noise can corrupt accurate information (for example, thermal noise, interference, and media noise arising from sources such as jitter, DC erase noise, and pulse width/height modulation). Media noise is a dominant source of noise in many current recording systems. The media noise is usually treated as highly correlated non-stationary noise added to a read-back signal. xe2x80x9cTransition jitterxe2x80x9d is the dominant component of media noise and affects the position of transitions.
RLL Coding schemes use (d, k) constraints, which limit a minimum and a maximum run lengths of zeros, respectively, or alternatively, the schemes control high and low frequency contents of user data. Conventional high-rate RLL (0, k) codes are highly complex for circuit implementation and relatively xe2x80x9cblindxe2x80x9d in terms of error detection during a demodulation process. The d, k constraints include properties of the conventional codes exploitable for error control purposes. However, this specialized type of error is only a small subset of the total number of possible errors.
A construction of an encoder, which encodes arbitrary binary sequences into sequences, is needed that obeys a specific run-length-limited (RLL) constraint. It is important that the encoder encodes data at a high rate, that the decoder does not propagate channel errors, and that a complexity of encoding and decoding be low.
White noise is added to every symbol entering a channel in a magnetic recording medium. Media Noise, like white noise, is random. Unlike the white noise, the media noise is not added to every symbol. The media noise happens only when there is a transition on the input to the channel. For example, if we input 00010110, then we have media noise when the input changes from a xe2x80x9c0xe2x80x9d to a xe2x80x9c1xe2x80x9d and from a xe2x80x9c1xe2x80x9d to a xe2x80x9c0xe2x80x9d. The denser a signal is written onto the magnetic recording medium, the more severe media noise becomes. Thus, a recording density controls a ratio of media noise to white noise. For instance, a ratio of 50:50 may be one example.
Let n_j, n_w, and n_e to denote components of media noise, n, due to jitter, j, pulse width noise, w, and electronic noise, e, respectively.
n=nxe2x80x94j+nxe2x80x94w+nxe2x80x94e+nxe2x80x2, where, nxe2x80x2, represents all other noises.
Components n_j and n_w are proportional to a number of pairs, (x(i), x(i+1)), that are (0, 1) or (1,0). In other words, n_j and n_w, are proportional to a number of times there is a transition in the x sequence either from 0 to 1, or from 1 to 0. Because, n_j and n_w depend on input data, the error performance of the system can vary significantly with the data. Sequences, x, having few transitions will suffer less from, n_j and n_w, than those having many transitions. Accordingly, an encoder is needed to reduce media noise from being added to an input of the channel x(i).
Various objects and advantages of the invention will be set forth in part in the description that follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
According to one aspect, an apparatus has a conversion circuit, a precoder circuit and a selection circuit. The conversion circuit converts user data b1, b2, b3 . . . bk to a coded sequence c0, c1, c2 . . . cq. The precoder circuit having an initial state (s2(0), s1(0)) produces an output x0, x1, x2 . . . xq from the coded sequence c0, c1, c2 . . . cq as follows: x(i)=c(i)⊕s2(ixe2x88x922), where (x(xe2x88x922), x(xe2x88x921))=(s2(0), s1(0)).
The selection circuit selects c0 in the coded sequence c0, c1, c2 . . . cq such that the output x0, x1, x2 . . . xq of the precoder circuit has less than a maximum number q of transitions.
The conversion circuit may include an encoder circuit to convert user data b1, b2, b3 . . . bk to a sequence c1, c2 . . . cq, and a transition minimization circuit to add c0 to the sequence c1, c2 . . . cq.
The apparatus may have a circuit to append the coded sequence c0, c1, c2 . . . cq by adding at least one additional bit to the coded sequence c0, c1, c2 . . . cq to produce a sequence c0, c1, c2, . . . , cq, cq+1, . . . , cm. The at least one additional bit added to produce c0, c1, c2, . . . , cq, cq+1, . . . , cm may include a parity bit.
According to another aspect, a method for coding includes adding a single bit to a input sequence of length q, and producing an output sequence of length q+1 having t transitions such that for any input sequence, t is an integer less than or equal to one half the maximum number of transitions and is represented by the following formula: txe2x89xa6q/2.
A computer readable medium may store a program for controlling at least one computer to perform the method.
These together with other aspects and advantages which will be subsequently apparent, reside in the details of construction and operation as more fully hereinafter described and claimed, reference being had to the accompanying drawings forming a part hereof, wherein like numerals refer to like parts throughout.